Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.81086 | −1.98758 | −0.993788 | − | 0.111293i | \(-0.964501\pi\) | ||||
−0.993788 | + | 0.111293i | \(0.964501\pi\) | |||||||
\(3\) | −2.68213 | −1.54853 | −0.774265 | − | 0.632861i | \(-0.781880\pi\) | ||||
−0.774265 | + | 0.632861i | \(0.781880\pi\) | |||||||
\(4\) | 5.90091 | 2.95046 | ||||||||
\(5\) | 2.99603 | 1.33986 | 0.669932 | − | 0.742423i | \(-0.266323\pi\) | ||||
0.669932 | + | 0.742423i | \(0.266323\pi\) | |||||||
\(6\) | 7.53909 | 3.07782 | ||||||||
\(7\) | 4.86255 | 1.83787 | 0.918936 | − | 0.394407i | \(-0.129050\pi\) | ||||
0.918936 | + | 0.394407i | \(0.129050\pi\) | |||||||
\(8\) | −10.9649 | −3.87668 | ||||||||
\(9\) | 4.19384 | 1.39795 | ||||||||
\(10\) | −8.42140 | −2.66308 | ||||||||
\(11\) | −1.33120 | −0.401371 | −0.200686 | − | 0.979656i | \(-0.564317\pi\) | ||||
−0.200686 | + | 0.979656i | \(0.564317\pi\) | |||||||
\(12\) | −15.8270 | −4.56887 | ||||||||
\(13\) | −3.27896 | −0.909421 | −0.454710 | − | 0.890639i | \(-0.650257\pi\) | ||||
−0.454710 | + | 0.890639i | \(0.650257\pi\) | |||||||
\(14\) | −13.6679 | −3.65291 | ||||||||
\(15\) | −8.03574 | −2.07482 | ||||||||
\(16\) | 19.0189 | 4.75473 | ||||||||
\(17\) | −4.03462 | −0.978539 | −0.489270 | − | 0.872133i | \(-0.662737\pi\) | ||||
−0.489270 | + | 0.872133i | \(0.662737\pi\) | |||||||
\(18\) | −11.7883 | −2.77852 | ||||||||
\(19\) | 4.45868 | 1.02289 | 0.511446 | − | 0.859315i | \(-0.329110\pi\) | ||||
0.511446 | + | 0.859315i | \(0.329110\pi\) | |||||||
\(20\) | 17.6793 | 3.95321 | ||||||||
\(21\) | −13.0420 | −2.84600 | ||||||||
\(22\) | 3.74181 | 0.797756 | ||||||||
\(23\) | −1.35388 | −0.282304 | −0.141152 | − | 0.989988i | \(-0.545081\pi\) | ||||
−0.141152 | + | 0.989988i | \(0.545081\pi\) | |||||||
\(24\) | 29.4093 | 6.00315 | ||||||||
\(25\) | 3.97617 | 0.795235 | ||||||||
\(26\) | 9.21669 | 1.80754 | ||||||||
\(27\) | −3.20203 | −0.616232 | ||||||||
\(28\) | 28.6935 | 5.42256 | ||||||||
\(29\) | 5.93104 | 1.10137 | 0.550683 | − | 0.834714i | \(-0.314367\pi\) | ||||
0.550683 | + | 0.834714i | \(0.314367\pi\) | |||||||
\(30\) | 22.5873 | 4.12386 | ||||||||
\(31\) | −2.35996 | −0.423861 | −0.211930 | − | 0.977285i | \(-0.567975\pi\) | ||||
−0.211930 | + | 0.977285i | \(0.567975\pi\) | |||||||
\(32\) | −31.5296 | −5.57371 | ||||||||
\(33\) | 3.57045 | 0.621536 | ||||||||
\(34\) | 11.3407 | 1.94492 | ||||||||
\(35\) | 14.5683 | 2.46250 | ||||||||
\(36\) | 24.7475 | 4.12458 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −12.5327 | −2.03308 | ||||||||
\(39\) | 8.79462 | 1.40827 | ||||||||
\(40\) | −32.8511 | −5.19422 | ||||||||
\(41\) | −7.42395 | −1.15943 | −0.579713 | − | 0.814821i | \(-0.696835\pi\) | ||||
−0.579713 | + | 0.814821i | \(0.696835\pi\) | |||||||
\(42\) | 36.6592 | 5.65664 | ||||||||
\(43\) | −4.67678 | −0.713203 | −0.356601 | − | 0.934257i | \(-0.616065\pi\) | ||||
−0.356601 | + | 0.934257i | \(0.616065\pi\) | |||||||
\(44\) | −7.85528 | −1.18423 | ||||||||
\(45\) | 12.5649 | 1.87306 | ||||||||
\(46\) | 3.80557 | 0.561101 | ||||||||
\(47\) | −7.56953 | −1.10413 | −0.552064 | − | 0.833801i | \(-0.686160\pi\) | ||||
−0.552064 | + | 0.833801i | \(0.686160\pi\) | |||||||
\(48\) | −51.0113 | −7.36284 | ||||||||
\(49\) | 16.6444 | 2.37777 | ||||||||
\(50\) | −11.1764 | −1.58059 | ||||||||
\(51\) | 10.8214 | 1.51530 | ||||||||
\(52\) | −19.3489 | −2.68321 | ||||||||
\(53\) | 2.65719 | 0.364994 | 0.182497 | − | 0.983206i | \(-0.441582\pi\) | ||||
0.182497 | + | 0.983206i | \(0.441582\pi\) | |||||||
\(54\) | 9.00046 | 1.22481 | ||||||||
\(55\) | −3.98830 | −0.537783 | ||||||||
\(56\) | −53.3174 | −7.12483 | ||||||||
\(57\) | −11.9588 | −1.58398 | ||||||||
\(58\) | −16.6713 | −2.18905 | ||||||||
\(59\) | −5.14063 | −0.669254 | −0.334627 | − | 0.942351i | \(-0.608610\pi\) | ||||
−0.334627 | + | 0.942351i | \(0.608610\pi\) | |||||||
\(60\) | −47.4182 | −6.12166 | ||||||||
\(61\) | −13.5372 | −1.73326 | −0.866628 | − | 0.498954i | \(-0.833718\pi\) | ||||
−0.866628 | + | 0.498954i | \(0.833718\pi\) | |||||||
\(62\) | 6.63350 | 0.842455 | ||||||||
\(63\) | 20.3928 | 2.56925 | ||||||||
\(64\) | 50.5875 | 6.32343 | ||||||||
\(65\) | −9.82386 | −1.21850 | ||||||||
\(66\) | −10.0360 | −1.23535 | ||||||||
\(67\) | −14.4823 | −1.76930 | −0.884650 | − | 0.466256i | \(-0.845603\pi\) | ||||
−0.884650 | + | 0.466256i | \(0.845603\pi\) | |||||||
\(68\) | −23.8079 | −2.88714 | ||||||||
\(69\) | 3.63129 | 0.437156 | ||||||||
\(70\) | −40.9495 | −4.89440 | ||||||||
\(71\) | −11.0342 | −1.30952 | −0.654758 | − | 0.755839i | \(-0.727229\pi\) | ||||
−0.654758 | + | 0.755839i | \(0.727229\pi\) | |||||||
\(72\) | −45.9850 | −5.41938 | ||||||||
\(73\) | 7.04248 | 0.824260 | 0.412130 | − | 0.911125i | \(-0.364785\pi\) | ||||
0.412130 | + | 0.911125i | \(0.364785\pi\) | |||||||
\(74\) | 2.81086 | 0.326755 | ||||||||
\(75\) | −10.6646 | −1.23144 | ||||||||
\(76\) | 26.3103 | 3.01800 | ||||||||
\(77\) | −6.47302 | −0.737669 | ||||||||
\(78\) | −24.7204 | −2.79903 | ||||||||
\(79\) | 14.1106 | 1.58757 | 0.793783 | − | 0.608201i | \(-0.208108\pi\) | ||||
0.793783 | + | 0.608201i | \(0.208108\pi\) | |||||||
\(80\) | 56.9812 | 6.37069 | ||||||||
\(81\) | −3.99323 | −0.443693 | ||||||||
\(82\) | 20.8676 | 2.30445 | ||||||||
\(83\) | 2.53040 | 0.277748 | 0.138874 | − | 0.990310i | \(-0.455652\pi\) | ||||
0.138874 | + | 0.990310i | \(0.455652\pi\) | |||||||
\(84\) | −76.9597 | −8.39700 | ||||||||
\(85\) | −12.0878 | −1.31111 | ||||||||
\(86\) | 13.1458 | 1.41754 | ||||||||
\(87\) | −15.9078 | −1.70550 | ||||||||
\(88\) | 14.5965 | 1.55599 | ||||||||
\(89\) | 1.25085 | 0.132590 | 0.0662948 | − | 0.997800i | \(-0.478882\pi\) | ||||
0.0662948 | + | 0.997800i | \(0.478882\pi\) | |||||||
\(90\) | −35.3180 | −3.72284 | ||||||||
\(91\) | −15.9441 | −1.67140 | ||||||||
\(92\) | −7.98914 | −0.832926 | ||||||||
\(93\) | 6.32972 | 0.656361 | ||||||||
\(94\) | 21.2768 | 2.19454 | ||||||||
\(95\) | 13.3583 | 1.37054 | ||||||||
\(96\) | 84.5667 | 8.63105 | ||||||||
\(97\) | −11.3637 | −1.15381 | −0.576906 | − | 0.816811i | \(-0.695740\pi\) | ||||
−0.576906 | + | 0.816811i | \(0.695740\pi\) | |||||||
\(98\) | −46.7850 | −4.72600 | ||||||||
\(99\) | −5.58283 | −0.561096 | ||||||||
\(100\) | 23.4630 | 2.34630 | ||||||||
\(101\) | −3.23748 | −0.322141 | −0.161071 | − | 0.986943i | \(-0.551495\pi\) | ||||
−0.161071 | + | 0.986943i | \(0.551495\pi\) | |||||||
\(102\) | −30.4174 | −3.01177 | ||||||||
\(103\) | 6.92612 | 0.682451 | 0.341226 | − | 0.939981i | \(-0.389158\pi\) | ||||
0.341226 | + | 0.939981i | \(0.389158\pi\) | |||||||
\(104\) | 35.9535 | 3.52553 | ||||||||
\(105\) | −39.0742 | −3.81325 | ||||||||
\(106\) | −7.46899 | −0.725453 | ||||||||
\(107\) | 2.27249 | 0.219690 | 0.109845 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109845 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(108\) | −18.8949 | −1.81816 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 11.2105 | 1.06888 | ||||||||
\(111\) | 2.68213 | 0.254577 | ||||||||
\(112\) | 92.4805 | 8.73858 | ||||||||
\(113\) | −14.0491 | −1.32163 | −0.660814 | − | 0.750550i | \(-0.729789\pi\) | ||||
−0.660814 | + | 0.750550i | \(0.729789\pi\) | |||||||
\(114\) | 33.6144 | 3.14828 | ||||||||
\(115\) | −4.05627 | −0.378249 | ||||||||
\(116\) | 34.9985 | 3.24953 | ||||||||
\(117\) | −13.7514 | −1.27132 | ||||||||
\(118\) | 14.4496 | 1.33019 | ||||||||
\(119\) | −19.6186 | −1.79843 | ||||||||
\(120\) | 88.1111 | 8.04340 | ||||||||
\(121\) | −9.22791 | −0.838901 | ||||||||
\(122\) | 38.0510 | 3.44498 | ||||||||
\(123\) | 19.9120 | 1.79541 | ||||||||
\(124\) | −13.9259 | −1.25058 | ||||||||
\(125\) | −3.06741 | −0.274358 | ||||||||
\(126\) | −57.3211 | −5.10657 | ||||||||
\(127\) | −15.4797 | −1.37360 | −0.686799 | − | 0.726847i | \(-0.740985\pi\) | ||||
−0.686799 | + | 0.726847i | \(0.740985\pi\) | |||||||
\(128\) | −79.1347 | −6.99459 | ||||||||
\(129\) | 12.5438 | 1.10442 | ||||||||
\(130\) | 27.6135 | 2.42186 | ||||||||
\(131\) | −20.7811 | −1.81565 | −0.907825 | − | 0.419350i | \(-0.862258\pi\) | ||||
−0.907825 | + | 0.419350i | \(0.862258\pi\) | |||||||
\(132\) | 21.0689 | 1.83381 | ||||||||
\(133\) | 21.6806 | 1.87994 | ||||||||
\(134\) | 40.7078 | 3.51662 | ||||||||
\(135\) | −9.59338 | −0.825667 | ||||||||
\(136\) | 44.2392 | 3.79348 | ||||||||
\(137\) | 13.5445 | 1.15719 | 0.578593 | − | 0.815616i | \(-0.303602\pi\) | ||||
0.578593 | + | 0.815616i | \(0.303602\pi\) | |||||||
\(138\) | −10.2070 | −0.868881 | ||||||||
\(139\) | −9.82763 | −0.833568 | −0.416784 | − | 0.909005i | \(-0.636843\pi\) | ||||
−0.416784 | + | 0.909005i | \(0.636843\pi\) | |||||||
\(140\) | 85.9664 | 7.26549 | ||||||||
\(141\) | 20.3025 | 1.70978 | ||||||||
\(142\) | 31.0155 | 2.60276 | ||||||||
\(143\) | 4.36495 | 0.365015 | ||||||||
\(144\) | 79.7623 | 6.64686 | ||||||||
\(145\) | 17.7696 | 1.47568 | ||||||||
\(146\) | −19.7954 | −1.63828 | ||||||||
\(147\) | −44.6425 | −3.68205 | ||||||||
\(148\) | −5.90091 | −0.485052 | ||||||||
\(149\) | 16.7138 | 1.36925 | 0.684624 | − | 0.728896i | \(-0.259966\pi\) | ||||
0.684624 | + | 0.728896i | \(0.259966\pi\) | |||||||
\(150\) | 29.9767 | 2.44759 | ||||||||
\(151\) | −8.08426 | −0.657888 | −0.328944 | − | 0.944349i | \(-0.606693\pi\) | ||||
−0.328944 | + | 0.944349i | \(0.606693\pi\) | |||||||
\(152\) | −48.8890 | −3.96542 | ||||||||
\(153\) | −16.9205 | −1.36795 | ||||||||
\(154\) | 18.1947 | 1.46617 | ||||||||
\(155\) | −7.07049 | −0.567916 | ||||||||
\(156\) | 51.8962 | 4.15502 | ||||||||
\(157\) | 5.16429 | 0.412155 | 0.206078 | − | 0.978536i | \(-0.433930\pi\) | ||||
0.206078 | + | 0.978536i | \(0.433930\pi\) | |||||||
\(158\) | −39.6629 | −3.15541 | ||||||||
\(159\) | −7.12695 | −0.565204 | ||||||||
\(160\) | −94.4637 | −7.46801 | ||||||||
\(161\) | −6.58333 | −0.518839 | ||||||||
\(162\) | 11.2244 | 0.881872 | ||||||||
\(163\) | 9.19682 | 0.720351 | 0.360175 | − | 0.932885i | \(-0.382717\pi\) | ||||
0.360175 | + | 0.932885i | \(0.382717\pi\) | |||||||
\(164\) | −43.8080 | −3.42083 | ||||||||
\(165\) | 10.6972 | 0.832773 | ||||||||
\(166\) | −7.11259 | −0.552044 | ||||||||
\(167\) | 0.805841 | 0.0623579 | 0.0311789 | − | 0.999514i | \(-0.490074\pi\) | ||||
0.0311789 | + | 0.999514i | \(0.490074\pi\) | |||||||
\(168\) | 143.004 | 11.0330 | ||||||||
\(169\) | −2.24840 | −0.172954 | ||||||||
\(170\) | 33.9771 | 2.60593 | ||||||||
\(171\) | 18.6990 | 1.42995 | ||||||||
\(172\) | −27.5973 | −2.10427 | ||||||||
\(173\) | −20.6448 | −1.56959 | −0.784797 | − | 0.619753i | \(-0.787233\pi\) | ||||
−0.784797 | + | 0.619753i | \(0.787233\pi\) | |||||||
\(174\) | 44.7147 | 3.38981 | ||||||||
\(175\) | 19.3343 | 1.46154 | ||||||||
\(176\) | −25.3180 | −1.90841 | ||||||||
\(177\) | 13.7879 | 1.03636 | ||||||||
\(178\) | −3.51595 | −0.263532 | ||||||||
\(179\) | 6.21114 | 0.464243 | 0.232121 | − | 0.972687i | \(-0.425433\pi\) | ||||
0.232121 | + | 0.972687i | \(0.425433\pi\) | |||||||
\(180\) | 74.1441 | 5.52637 | ||||||||
\(181\) | −3.17195 | −0.235769 | −0.117885 | − | 0.993027i | \(-0.537611\pi\) | ||||
−0.117885 | + | 0.993027i | \(0.537611\pi\) | |||||||
\(182\) | 44.8166 | 3.32203 | ||||||||
\(183\) | 36.3085 | 2.68400 | ||||||||
\(184\) | 14.8452 | 1.09440 | ||||||||
\(185\) | −2.99603 | −0.220272 | ||||||||
\(186\) | −17.7919 | −1.30457 | ||||||||
\(187\) | 5.37088 | 0.392758 | ||||||||
\(188\) | −44.6671 | −3.25768 | ||||||||
\(189\) | −15.5701 | −1.13256 | ||||||||
\(190\) | −37.5484 | −2.72404 | ||||||||
\(191\) | −25.3004 | −1.83068 | −0.915338 | − | 0.402686i | \(-0.868077\pi\) | ||||
−0.915338 | + | 0.402686i | \(0.868077\pi\) | |||||||
\(192\) | −135.682 | −9.79203 | ||||||||
\(193\) | −8.60196 | −0.619182 | −0.309591 | − | 0.950870i | \(-0.600192\pi\) | ||||
−0.309591 | + | 0.950870i | \(0.600192\pi\) | |||||||
\(194\) | 31.9418 | 2.29329 | ||||||||
\(195\) | 26.3489 | 1.88688 | ||||||||
\(196\) | 98.2172 | 7.01551 | ||||||||
\(197\) | 4.89769 | 0.348946 | 0.174473 | − | 0.984662i | \(-0.444178\pi\) | ||||
0.174473 | + | 0.984662i | \(0.444178\pi\) | |||||||
\(198\) | 15.6925 | 1.11522 | ||||||||
\(199\) | −2.21511 | −0.157025 | −0.0785126 | − | 0.996913i | \(-0.525017\pi\) | ||||
−0.0785126 | + | 0.996913i | \(0.525017\pi\) | |||||||
\(200\) | −43.5983 | −3.08287 | ||||||||
\(201\) | 38.8436 | 2.73981 | ||||||||
\(202\) | 9.10009 | 0.640280 | ||||||||
\(203\) | 28.8400 | 2.02417 | ||||||||
\(204\) | 63.8560 | 4.47082 | ||||||||
\(205\) | −22.2423 | −1.55347 | ||||||||
\(206\) | −19.4683 | −1.35642 | ||||||||
\(207\) | −5.67797 | −0.394646 | ||||||||
\(208\) | −62.3623 | −4.32405 | ||||||||
\(209\) | −5.93539 | −0.410560 | ||||||||
\(210\) | 109.832 | 7.57913 | ||||||||
\(211\) | 17.7341 | 1.22087 | 0.610433 | − | 0.792068i | \(-0.290995\pi\) | ||||
0.610433 | + | 0.792068i | \(0.290995\pi\) | |||||||
\(212\) | 15.6799 | 1.07690 | ||||||||
\(213\) | 29.5951 | 2.02782 | ||||||||
\(214\) | −6.38765 | −0.436651 | ||||||||
\(215\) | −14.0118 | −0.955594 | ||||||||
\(216\) | 35.1100 | 2.38893 | ||||||||
\(217\) | −11.4754 | −0.779002 | ||||||||
\(218\) | 2.81086 | 0.190375 | ||||||||
\(219\) | −18.8889 | −1.27639 | ||||||||
\(220\) | −23.5346 | −1.58670 | ||||||||
\(221\) | 13.2294 | 0.889904 | ||||||||
\(222\) | −7.53909 | −0.505991 | ||||||||
\(223\) | −17.4275 | −1.16703 | −0.583517 | − | 0.812101i | \(-0.698324\pi\) | ||||
−0.583517 | + | 0.812101i | \(0.698324\pi\) | |||||||
\(224\) | −153.315 | −10.2438 | ||||||||
\(225\) | 16.6754 | 1.11170 | ||||||||
\(226\) | 39.4900 | 2.62683 | ||||||||
\(227\) | −4.26191 | −0.282873 | −0.141436 | − | 0.989947i | \(-0.545172\pi\) | ||||
−0.141436 | + | 0.989947i | \(0.545172\pi\) | |||||||
\(228\) | −70.5677 | −4.67346 | ||||||||
\(229\) | 18.5238 | 1.22409 | 0.612045 | − | 0.790823i | \(-0.290347\pi\) | ||||
0.612045 | + | 0.790823i | \(0.290347\pi\) | |||||||
\(230\) | 11.4016 | 0.751798 | ||||||||
\(231\) | 17.3615 | 1.14230 | ||||||||
\(232\) | −65.0333 | −4.26964 | ||||||||
\(233\) | 13.2639 | 0.868949 | 0.434474 | − | 0.900684i | \(-0.356934\pi\) | ||||
0.434474 | + | 0.900684i | \(0.356934\pi\) | |||||||
\(234\) | 38.6533 | 2.52685 | ||||||||
\(235\) | −22.6785 | −1.47938 | ||||||||
\(236\) | −30.3344 | −1.97460 | ||||||||
\(237\) | −37.8465 | −2.45839 | ||||||||
\(238\) | 55.1449 | 3.57451 | ||||||||
\(239\) | 1.16799 | 0.0755509 | 0.0377755 | − | 0.999286i | \(-0.487973\pi\) | ||||
0.0377755 | + | 0.999286i | \(0.487973\pi\) | |||||||
\(240\) | −152.831 | −9.86521 | ||||||||
\(241\) | 17.7842 | 1.14558 | 0.572790 | − | 0.819702i | \(-0.305861\pi\) | ||||
0.572790 | + | 0.819702i | \(0.305861\pi\) | |||||||
\(242\) | 25.9383 | 1.66738 | ||||||||
\(243\) | 20.3165 | 1.30330 | ||||||||
\(244\) | −79.8816 | −5.11390 | ||||||||
\(245\) | 49.8671 | 3.18589 | ||||||||
\(246\) | −55.9698 | −3.56850 | ||||||||
\(247\) | −14.6199 | −0.930240 | ||||||||
\(248\) | 25.8767 | 1.64317 | ||||||||
\(249\) | −6.78687 | −0.430100 | ||||||||
\(250\) | 8.62205 | 0.545307 | ||||||||
\(251\) | −15.0140 | −0.947672 | −0.473836 | − | 0.880613i | \(-0.657131\pi\) | ||||
−0.473836 | + | 0.880613i | \(0.657131\pi\) | |||||||
\(252\) | 120.336 | 7.58044 | ||||||||
\(253\) | 1.80229 | 0.113309 | ||||||||
\(254\) | 43.5111 | 2.73013 | ||||||||
\(255\) | 32.4212 | 2.03029 | ||||||||
\(256\) | 121.261 | 7.57884 | ||||||||
\(257\) | −2.14831 | −0.134008 | −0.0670039 | − | 0.997753i | \(-0.521344\pi\) | ||||
−0.0670039 | + | 0.997753i | \(0.521344\pi\) | |||||||
\(258\) | −35.2587 | −2.19511 | ||||||||
\(259\) | −4.86255 | −0.302144 | ||||||||
\(260\) | −57.9697 | −3.59513 | ||||||||
\(261\) | 24.8738 | 1.53965 | ||||||||
\(262\) | 58.4125 | 3.60874 | ||||||||
\(263\) | −0.0603126 | −0.00371903 | −0.00185952 | − | 0.999998i | \(-0.500592\pi\) | ||||
−0.00185952 | + | 0.999998i | \(0.500592\pi\) | |||||||
\(264\) | −39.1496 | −2.40949 | ||||||||
\(265\) | 7.96102 | 0.489042 | ||||||||
\(266\) | −60.9410 | −3.73653 | ||||||||
\(267\) | −3.35494 | −0.205319 | ||||||||
\(268\) | −85.4590 | −5.22024 | ||||||||
\(269\) | 25.9608 | 1.58286 | 0.791430 | − | 0.611260i | \(-0.209337\pi\) | ||||
0.791430 | + | 0.611260i | \(0.209337\pi\) | |||||||
\(270\) | 26.9656 | 1.64107 | ||||||||
\(271\) | −2.16211 | −0.131339 | −0.0656694 | − | 0.997841i | \(-0.520918\pi\) | ||||
−0.0656694 | + | 0.997841i | \(0.520918\pi\) | |||||||
\(272\) | −76.7341 | −4.65269 | ||||||||
\(273\) | 42.7643 | 2.58821 | ||||||||
\(274\) | −38.0717 | −2.30000 | ||||||||
\(275\) | −5.29307 | −0.319184 | ||||||||
\(276\) | 21.4279 | 1.28981 | ||||||||
\(277\) | 2.49388 | 0.149842 | 0.0749212 | − | 0.997189i | \(-0.476129\pi\) | ||||
0.0749212 | + | 0.997189i | \(0.476129\pi\) | |||||||
\(278\) | 27.6240 | 1.65678 | ||||||||
\(279\) | −9.89728 | −0.592535 | ||||||||
\(280\) | −159.740 | −9.54631 | ||||||||
\(281\) | 24.6016 | 1.46761 | 0.733805 | − | 0.679360i | \(-0.237743\pi\) | ||||
0.733805 | + | 0.679360i | \(0.237743\pi\) | |||||||
\(282\) | −57.0673 | −3.39831 | ||||||||
\(283\) | −30.5285 | −1.81473 | −0.907367 | − | 0.420339i | \(-0.861911\pi\) | ||||
−0.907367 | + | 0.420339i | \(0.861911\pi\) | |||||||
\(284\) | −65.1116 | −3.86367 | ||||||||
\(285\) | −35.8288 | −2.12232 | ||||||||
\(286\) | −12.2692 | −0.725496 | ||||||||
\(287\) | −36.0993 | −2.13088 | ||||||||
\(288\) | −132.230 | −7.79174 | ||||||||
\(289\) | −0.721838 | −0.0424611 | ||||||||
\(290\) | −49.9477 | −2.93303 | ||||||||
\(291\) | 30.4790 | 1.78671 | ||||||||
\(292\) | 41.5570 | 2.43194 | ||||||||
\(293\) | 5.32044 | 0.310824 | 0.155412 | − | 0.987850i | \(-0.450330\pi\) | ||||
0.155412 | + | 0.987850i | \(0.450330\pi\) | |||||||
\(294\) | 125.484 | 7.31836 | ||||||||
\(295\) | −15.4015 | −0.896709 | ||||||||
\(296\) | 10.9649 | 0.637322 | ||||||||
\(297\) | 4.26254 | 0.247338 | ||||||||
\(298\) | −46.9801 | −2.72148 | ||||||||
\(299\) | 4.43933 | 0.256733 | ||||||||
\(300\) | −62.9310 | −3.63332 | ||||||||
\(301\) | −22.7411 | −1.31077 | ||||||||
\(302\) | 22.7237 | 1.30760 | ||||||||
\(303\) | 8.68335 | 0.498845 | ||||||||
\(304\) | 84.7994 | 4.86358 | ||||||||
\(305\) | −40.5577 | −2.32233 | ||||||||
\(306\) | 47.5612 | 2.71889 | ||||||||
\(307\) | 10.6136 | 0.605753 | 0.302876 | − | 0.953030i | \(-0.402053\pi\) | ||||
0.302876 | + | 0.953030i | \(0.402053\pi\) | |||||||
\(308\) | −38.1967 | −2.17646 | ||||||||
\(309\) | −18.5768 | −1.05680 | ||||||||
\(310\) | 19.8741 | 1.12878 | ||||||||
\(311\) | 21.3873 | 1.21276 | 0.606381 | − | 0.795174i | \(-0.292621\pi\) | ||||
0.606381 | + | 0.795174i | \(0.292621\pi\) | |||||||
\(312\) | −96.4321 | −5.45939 | ||||||||
\(313\) | −18.5621 | −1.04919 | −0.524597 | − | 0.851351i | \(-0.675784\pi\) | ||||
−0.524597 | + | 0.851351i | \(0.675784\pi\) | |||||||
\(314\) | −14.5161 | −0.819189 | ||||||||
\(315\) | 61.0972 | 3.44244 | ||||||||
\(316\) | 83.2654 | 4.68404 | ||||||||
\(317\) | 1.20282 | 0.0675573 | 0.0337787 | − | 0.999429i | \(-0.489246\pi\) | ||||
0.0337787 | + | 0.999429i | \(0.489246\pi\) | |||||||
\(318\) | 20.0328 | 1.12339 | ||||||||
\(319\) | −7.89539 | −0.442057 | ||||||||
\(320\) | 151.561 | 8.47254 | ||||||||
\(321\) | −6.09513 | −0.340197 | ||||||||
\(322\) | 18.5048 | 1.03123 | ||||||||
\(323\) | −17.9891 | −1.00094 | ||||||||
\(324\) | −23.5637 | −1.30909 | ||||||||
\(325\) | −13.0377 | −0.723203 | ||||||||
\(326\) | −25.8509 | −1.43175 | ||||||||
\(327\) | 2.68213 | 0.148322 | ||||||||
\(328\) | 81.4028 | 4.49472 | ||||||||
\(329\) | −36.8072 | −2.02925 | ||||||||
\(330\) | −30.0682 | −1.65520 | ||||||||
\(331\) | −11.0526 | −0.607508 | −0.303754 | − | 0.952750i | \(-0.598240\pi\) | ||||
−0.303754 | + | 0.952750i | \(0.598240\pi\) | |||||||
\(332\) | 14.9317 | 0.819482 | ||||||||
\(333\) | −4.19384 | −0.229821 | ||||||||
\(334\) | −2.26510 | −0.123941 | ||||||||
\(335\) | −43.3895 | −2.37062 | ||||||||
\(336\) | −248.045 | −13.5320 | ||||||||
\(337\) | 6.27586 | 0.341868 | 0.170934 | − | 0.985282i | \(-0.445322\pi\) | ||||
0.170934 | + | 0.985282i | \(0.445322\pi\) | |||||||
\(338\) | 6.31993 | 0.343759 | ||||||||
\(339\) | 37.6816 | 2.04658 | ||||||||
\(340\) | −71.3292 | −3.86837 | ||||||||
\(341\) | 3.14157 | 0.170126 | ||||||||
\(342\) | −52.5602 | −2.84213 | ||||||||
\(343\) | 46.8964 | 2.53217 | ||||||||
\(344\) | 51.2804 | 2.76486 | ||||||||
\(345\) | 10.8795 | 0.585730 | ||||||||
\(346\) | 58.0295 | 3.11969 | ||||||||
\(347\) | 9.86961 | 0.529828 | 0.264914 | − | 0.964272i | \(-0.414656\pi\) | ||||
0.264914 | + | 0.964272i | \(0.414656\pi\) | |||||||
\(348\) | −93.8708 | −5.03200 | ||||||||
\(349\) | −7.92123 | −0.424014 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
−0.212007 | + | 0.977268i | \(0.568000\pi\) | |||||||
\(350\) | −54.3461 | −2.90492 | ||||||||
\(351\) | 10.4994 | 0.560414 | ||||||||
\(352\) | 41.9722 | 2.23713 | ||||||||
\(353\) | 16.5909 | 0.883043 | 0.441521 | − | 0.897251i | \(-0.354439\pi\) | ||||
0.441521 | + | 0.897251i | \(0.354439\pi\) | |||||||
\(354\) | −38.7557 | −2.05984 | ||||||||
\(355\) | −33.0587 | −1.75457 | ||||||||
\(356\) | 7.38114 | 0.391199 | ||||||||
\(357\) | 52.6196 | 2.78492 | ||||||||
\(358\) | −17.4586 | −0.922717 | ||||||||
\(359\) | 25.4669 | 1.34409 | 0.672045 | − | 0.740510i | \(-0.265416\pi\) | ||||
0.672045 | + | 0.740510i | \(0.265416\pi\) | |||||||
\(360\) | −137.772 | −7.26124 | ||||||||
\(361\) | 0.879864 | 0.0463086 | ||||||||
\(362\) | 8.91590 | 0.468609 | ||||||||
\(363\) | 24.7505 | 1.29906 | ||||||||
\(364\) | −94.0849 | −4.93139 | ||||||||
\(365\) | 21.0995 | 1.10440 | ||||||||
\(366\) | −102.058 | −5.33465 | ||||||||
\(367\) | 26.7846 | 1.39814 | 0.699072 | − | 0.715051i | \(-0.253597\pi\) | ||||
0.699072 | + | 0.715051i | \(0.253597\pi\) | |||||||
\(368\) | −25.7494 | −1.34228 | ||||||||
\(369\) | −31.1348 | −1.62081 | ||||||||
\(370\) | 8.42140 | 0.437808 | ||||||||
\(371\) | 12.9207 | 0.670812 | ||||||||
\(372\) | 37.3511 | 1.93656 | ||||||||
\(373\) | −6.31516 | −0.326986 | −0.163493 | − | 0.986544i | \(-0.552276\pi\) | ||||
−0.163493 | + | 0.986544i | \(0.552276\pi\) | |||||||
\(374\) | −15.0968 | −0.780635 | ||||||||
\(375\) | 8.22721 | 0.424851 | ||||||||
\(376\) | 82.9991 | 4.28035 | ||||||||
\(377\) | −19.4477 | −1.00161 | ||||||||
\(378\) | 43.7652 | 2.25104 | ||||||||
\(379\) | 0.633469 | 0.0325391 | 0.0162696 | − | 0.999868i | \(-0.494821\pi\) | ||||
0.0162696 | + | 0.999868i | \(0.494821\pi\) | |||||||
\(380\) | 78.8263 | 4.04371 | ||||||||
\(381\) | 41.5185 | 2.12706 | ||||||||
\(382\) | 71.1159 | 3.63861 | ||||||||
\(383\) | −30.6755 | −1.56744 | −0.783722 | − | 0.621112i | \(-0.786681\pi\) | ||||
−0.783722 | + | 0.621112i | \(0.786681\pi\) | |||||||
\(384\) | 212.250 | 10.8313 | ||||||||
\(385\) | −19.3933 | −0.988376 | ||||||||
\(386\) | 24.1789 | 1.23067 | ||||||||
\(387\) | −19.6137 | −0.997019 | ||||||||
\(388\) | −67.0564 | −3.40427 | ||||||||
\(389\) | −20.4414 | −1.03642 | −0.518211 | − | 0.855253i | \(-0.673402\pi\) | ||||
−0.518211 | + | 0.855253i | \(0.673402\pi\) | |||||||
\(390\) | −74.0630 | −3.75032 | ||||||||
\(391\) | 5.46240 | 0.276246 | ||||||||
\(392\) | −182.504 | −9.21786 | ||||||||
\(393\) | 55.7376 | 2.81159 | ||||||||
\(394\) | −13.7667 | −0.693556 | ||||||||
\(395\) | 42.2757 | 2.12712 | ||||||||
\(396\) | −32.9438 | −1.65549 | ||||||||
\(397\) | 13.3793 | 0.671489 | 0.335745 | − | 0.941953i | \(-0.391012\pi\) | ||||
0.335745 | + | 0.941953i | \(0.391012\pi\) | |||||||
\(398\) | 6.22636 | 0.312099 | ||||||||
\(399\) | −58.1502 | −2.91115 | ||||||||
\(400\) | 75.6225 | 3.78113 | ||||||||
\(401\) | 20.8625 | 1.04182 | 0.520912 | − | 0.853610i | \(-0.325592\pi\) | ||||
0.520912 | + | 0.853610i | \(0.325592\pi\) | |||||||
\(402\) | −109.184 | −5.44559 | ||||||||
\(403\) | 7.73821 | 0.385468 | ||||||||
\(404\) | −19.1041 | −0.950463 | ||||||||
\(405\) | −11.9638 | −0.594487 | ||||||||
\(406\) | −81.0651 | −4.02319 | ||||||||
\(407\) | 1.33120 | 0.0659850 | ||||||||
\(408\) | −118.655 | −5.87432 | ||||||||
\(409\) | 18.9188 | 0.935473 | 0.467736 | − | 0.883868i | \(-0.345070\pi\) | ||||
0.467736 | + | 0.883868i | \(0.345070\pi\) | |||||||
\(410\) | 62.5200 | 3.08764 | ||||||||
\(411\) | −36.3282 | −1.79194 | ||||||||
\(412\) | 40.8704 | 2.01354 | ||||||||
\(413\) | −24.9966 | −1.23000 | ||||||||
\(414\) | 15.9599 | 0.784389 | ||||||||
\(415\) | 7.58115 | 0.372144 | ||||||||
\(416\) | 103.385 | 5.06885 | ||||||||
\(417\) | 26.3590 | 1.29081 | ||||||||
\(418\) | 16.6835 | 0.816018 | ||||||||
\(419\) | 6.28932 | 0.307253 | 0.153627 | − | 0.988129i | \(-0.450905\pi\) | ||||
0.153627 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(420\) | −230.573 | −11.2508 | ||||||||
\(421\) | −3.87669 | −0.188938 | −0.0944691 | − | 0.995528i | \(-0.530115\pi\) | ||||
−0.0944691 | + | 0.995528i | \(0.530115\pi\) | |||||||
\(422\) | −49.8480 | −2.42656 | ||||||||
\(423\) | −31.7454 | −1.54351 | ||||||||
\(424\) | −29.1359 | −1.41496 | ||||||||
\(425\) | −16.0423 | −0.778168 | ||||||||
\(426\) | −83.1876 | −4.03045 | ||||||||
\(427\) | −65.8252 | −3.18550 | ||||||||
\(428\) | 13.4098 | 0.648186 | ||||||||
\(429\) | −11.7074 | −0.565238 | ||||||||
\(430\) | 39.3850 | 1.89932 | ||||||||
\(431\) | −34.9383 | −1.68292 | −0.841459 | − | 0.540320i | \(-0.818303\pi\) | ||||
−0.841459 | + | 0.540320i | \(0.818303\pi\) | |||||||
\(432\) | −60.8992 | −2.93002 | ||||||||
\(433\) | −5.20144 | −0.249965 | −0.124983 | − | 0.992159i | \(-0.539888\pi\) | ||||
−0.124983 | + | 0.992159i | \(0.539888\pi\) | |||||||
\(434\) | 32.2557 | 1.54832 | ||||||||
\(435\) | −47.6603 | −2.28514 | ||||||||
\(436\) | −5.90091 | −0.282602 | ||||||||
\(437\) | −6.03654 | −0.288767 | ||||||||
\(438\) | 53.0939 | 2.53692 | ||||||||
\(439\) | 21.3471 | 1.01884 | 0.509421 | − | 0.860518i | \(-0.329860\pi\) | ||||
0.509421 | + | 0.860518i | \(0.329860\pi\) | |||||||
\(440\) | 43.7313 | 2.08481 | ||||||||
\(441\) | 69.8040 | 3.32400 | ||||||||
\(442\) | −37.1859 | −1.76875 | ||||||||
\(443\) | 38.9121 | 1.84877 | 0.924386 | − | 0.381459i | \(-0.124578\pi\) | ||||
0.924386 | + | 0.381459i | \(0.124578\pi\) | |||||||
\(444\) | 15.8270 | 0.751117 | ||||||||
\(445\) | 3.74757 | 0.177652 | ||||||||
\(446\) | 48.9863 | 2.31957 | ||||||||
\(447\) | −44.8286 | −2.12032 | ||||||||
\(448\) | 245.984 | 11.6217 | ||||||||
\(449\) | −2.39938 | −0.113234 | −0.0566170 | − | 0.998396i | \(-0.518031\pi\) | ||||
−0.0566170 | + | 0.998396i | \(0.518031\pi\) | |||||||
\(450\) | −46.8722 | −2.20958 | ||||||||
\(451\) | 9.88274 | 0.465360 | ||||||||
\(452\) | −82.9025 | −3.89940 | ||||||||
\(453\) | 21.6831 | 1.01876 | ||||||||
\(454\) | 11.9796 | 0.562231 | ||||||||
\(455\) | −47.7690 | −2.23945 | ||||||||
\(456\) | 131.127 | 6.14058 | ||||||||
\(457\) | 26.3377 | 1.23203 | 0.616014 | − | 0.787735i | \(-0.288746\pi\) | ||||
0.616014 | + | 0.787735i | \(0.288746\pi\) | |||||||
\(458\) | −52.0678 | −2.43297 | ||||||||
\(459\) | 12.9190 | 0.603007 | ||||||||
\(460\) | −23.9357 | −1.11601 | ||||||||
\(461\) | −6.62506 | −0.308560 | −0.154280 | − | 0.988027i | \(-0.549306\pi\) | ||||
−0.154280 | + | 0.988027i | \(0.549306\pi\) | |||||||
\(462\) | −48.8007 | −2.27041 | ||||||||
\(463\) | −5.93727 | −0.275929 | −0.137964 | − | 0.990437i | \(-0.544056\pi\) | ||||
−0.137964 | + | 0.990437i | \(0.544056\pi\) | |||||||
\(464\) | 112.802 | 5.23670 | ||||||||
\(465\) | 18.9640 | 0.879435 | ||||||||
\(466\) | −37.2830 | −1.72710 | ||||||||
\(467\) | −22.5706 | −1.04444 | −0.522222 | − | 0.852810i | \(-0.674897\pi\) | ||||
−0.522222 | + | 0.852810i | \(0.674897\pi\) | |||||||
\(468\) | −81.1460 | −3.75098 | ||||||||
\(469\) | −70.4211 | −3.25175 | ||||||||
\(470\) | 63.7460 | 2.94038 | ||||||||
\(471\) | −13.8513 | −0.638235 | ||||||||
\(472\) | 56.3665 | 2.59448 | ||||||||
\(473\) | 6.22572 | 0.286259 | ||||||||
\(474\) | 106.381 | 4.88624 | ||||||||
\(475\) | 17.7285 | 0.813439 | ||||||||
\(476\) | −115.767 | −5.30619 | ||||||||
\(477\) | 11.1438 | 0.510242 | ||||||||
\(478\) | −3.28305 | −0.150163 | ||||||||
\(479\) | −41.1560 | −1.88047 | −0.940234 | − | 0.340530i | \(-0.889394\pi\) | ||||
−0.940234 | + | 0.340530i | \(0.889394\pi\) | |||||||
\(480\) | 253.364 | 11.5644 | ||||||||
\(481\) | 3.27896 | 0.149508 | ||||||||
\(482\) | −49.9888 | −2.27693 | ||||||||
\(483\) | 17.6574 | 0.803438 | ||||||||
\(484\) | −54.4531 | −2.47514 | ||||||||
\(485\) | −34.0460 | −1.54595 | ||||||||
\(486\) | −57.1067 | −2.59041 | ||||||||
\(487\) | −6.66629 | −0.302078 | −0.151039 | − | 0.988528i | \(-0.548262\pi\) | ||||
−0.151039 | + | 0.988528i | \(0.548262\pi\) | |||||||
\(488\) | 148.434 | 6.71927 | ||||||||
\(489\) | −24.6671 | −1.11548 | ||||||||
\(490\) | −140.169 | −6.33220 | ||||||||
\(491\) | −7.31656 | −0.330192 | −0.165096 | − | 0.986278i | \(-0.552793\pi\) | ||||
−0.165096 | + | 0.986278i | \(0.552793\pi\) | |||||||
\(492\) | 117.499 | 5.29726 | ||||||||
\(493\) | −23.9295 | −1.07773 | ||||||||
\(494\) | 41.0943 | 1.84892 | ||||||||
\(495\) | −16.7263 | −0.751792 | ||||||||
\(496\) | −44.8838 | −2.01534 | ||||||||
\(497\) | −53.6542 | −2.40672 | ||||||||
\(498\) | 19.0769 | 0.854857 | ||||||||
\(499\) | −18.1881 | −0.814209 | −0.407105 | − | 0.913382i | \(-0.633462\pi\) | ||||
−0.407105 | + | 0.913382i | \(0.633462\pi\) | |||||||
\(500\) | −18.1005 | −0.809480 | ||||||||
\(501\) | −2.16137 | −0.0965630 | ||||||||
\(502\) | 42.2021 | 1.88357 | ||||||||
\(503\) | −42.3410 | −1.88789 | −0.943945 | − | 0.330102i | \(-0.892917\pi\) | ||||
−0.943945 | + | 0.330102i | \(0.892917\pi\) | |||||||
\(504\) | −223.604 | −9.96013 | ||||||||
\(505\) | −9.69957 | −0.431625 | ||||||||
\(506\) | −5.06597 | −0.225210 | ||||||||
\(507\) | 6.03051 | 0.267824 | ||||||||
\(508\) | −91.3442 | −4.05274 | ||||||||
\(509\) | 23.9738 | 1.06262 | 0.531310 | − | 0.847178i | \(-0.321700\pi\) | ||||
0.531310 | + | 0.847178i | \(0.321700\pi\) | |||||||
\(510\) | −91.1312 | −4.03536 | ||||||||
\(511\) | 34.2444 | 1.51488 | ||||||||
\(512\) | −182.579 | −8.06892 | ||||||||
\(513\) | −14.2769 | −0.630339 | ||||||||
\(514\) | 6.03859 | 0.266351 | ||||||||
\(515\) | 20.7508 | 0.914392 | ||||||||
\(516\) | 74.0196 | 3.25853 | ||||||||
\(517\) | 10.0765 | 0.443166 | ||||||||
\(518\) | 13.6679 | 0.600534 | ||||||||
\(519\) | 55.3721 | 2.43056 | ||||||||
\(520\) | 107.718 | 4.72373 | ||||||||
\(521\) | −9.43141 | −0.413198 | −0.206599 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206599 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(522\) | −69.9168 | −3.06017 | ||||||||
\(523\) | 17.6670 | 0.772523 | 0.386262 | − | 0.922389i | \(-0.373766\pi\) | ||||
0.386262 | + | 0.922389i | \(0.373766\pi\) | |||||||
\(524\) | −122.627 | −5.35699 | ||||||||
\(525\) | −51.8573 | −2.26324 | ||||||||
\(526\) | 0.169530 | 0.00739186 | ||||||||
\(527\) | 9.52153 | 0.414764 | ||||||||
\(528\) | 67.9061 | 2.95523 | ||||||||
\(529\) | −21.1670 | −0.920304 | ||||||||
\(530\) | −22.3773 | −0.972007 | ||||||||
\(531\) | −21.5590 | −0.935581 | ||||||||
\(532\) | 127.935 | 5.54669 | ||||||||
\(533\) | 24.3428 | 1.05441 | ||||||||
\(534\) | 9.43025 | 0.408087 | ||||||||
\(535\) | 6.80845 | 0.294355 | ||||||||
\(536\) | 158.797 | 6.85900 | ||||||||
\(537\) | −16.6591 | −0.718894 | ||||||||
\(538\) | −72.9722 | −3.14605 | ||||||||
\(539\) | −22.1570 | −0.954370 | ||||||||
\(540\) | −56.6097 | −2.43609 | ||||||||
\(541\) | 12.4410 | 0.534881 | 0.267441 | − | 0.963574i | \(-0.413822\pi\) | ||||
0.267441 | + | 0.963574i | \(0.413822\pi\) | |||||||
\(542\) | 6.07738 | 0.261046 | ||||||||
\(543\) | 8.50760 | 0.365096 | ||||||||
\(544\) | 127.210 | 5.45409 | ||||||||
\(545\) | −2.99603 | −0.128336 | ||||||||
\(546\) | −120.204 | −5.14427 | ||||||||
\(547\) | 16.9857 | 0.726257 | 0.363128 | − | 0.931739i | \(-0.381709\pi\) | ||||
0.363128 | + | 0.931739i | \(0.381709\pi\) | |||||||
\(548\) | 79.9250 | 3.41423 | ||||||||
\(549\) | −56.7727 | −2.42300 | ||||||||
\(550\) | 14.8781 | 0.634403 | ||||||||
\(551\) | 26.4446 | 1.12658 | ||||||||
\(552\) | −39.8168 | −1.69471 | ||||||||
\(553\) | 68.6135 | 2.91774 | ||||||||
\(554\) | −7.00992 | −0.297823 | ||||||||
\(555\) | 8.03574 | 0.341098 | ||||||||
\(556\) | −57.9919 | −2.45941 | ||||||||
\(557\) | −12.2201 | −0.517783 | −0.258892 | − | 0.965906i | \(-0.583357\pi\) | ||||
−0.258892 | + | 0.965906i | \(0.583357\pi\) | |||||||
\(558\) | 27.8198 | 1.17771 | ||||||||
\(559\) | 15.3350 | 0.648601 | ||||||||
\(560\) | 277.074 | 11.7085 | ||||||||
\(561\) | −14.4054 | −0.608197 | ||||||||
\(562\) | −69.1516 | −2.91698 | ||||||||
\(563\) | −24.1750 | −1.01885 | −0.509426 | − | 0.860514i | \(-0.670142\pi\) | ||||
−0.509426 | + | 0.860514i | \(0.670142\pi\) | |||||||
\(564\) | 119.803 | 5.04462 | ||||||||
\(565\) | −42.0915 | −1.77080 | ||||||||
\(566\) | 85.8113 | 3.60692 | ||||||||
\(567\) | −19.4173 | −0.815450 | ||||||||
\(568\) | 120.989 | 5.07657 | ||||||||
\(569\) | 19.2414 | 0.806642 | 0.403321 | − | 0.915058i | \(-0.367856\pi\) | ||||
0.403321 | + | 0.915058i | \(0.367856\pi\) | |||||||
\(570\) | 100.710 | 4.21826 | ||||||||
\(571\) | 31.6459 | 1.32434 | 0.662169 | − | 0.749354i | \(-0.269636\pi\) | ||||
0.662169 | + | 0.749354i | \(0.269636\pi\) | |||||||
\(572\) | 25.7572 | 1.07696 | ||||||||
\(573\) | 67.8592 | 2.83486 | ||||||||
\(574\) | 101.470 | 4.23528 | ||||||||
\(575\) | −5.38327 | −0.224498 | ||||||||
\(576\) | 212.156 | 8.83982 | ||||||||
\(577\) | 17.4190 | 0.725164 | 0.362582 | − | 0.931952i | \(-0.381895\pi\) | ||||
0.362582 | + | 0.931952i | \(0.381895\pi\) | |||||||
\(578\) | 2.02898 | 0.0843946 | ||||||||
\(579\) | 23.0716 | 0.958823 | ||||||||
\(580\) | 104.857 | 4.35393 | ||||||||
\(581\) | 12.3042 | 0.510464 | ||||||||
\(582\) | −85.6722 | −3.55123 | ||||||||
\(583\) | −3.53725 | −0.146498 | ||||||||
\(584\) | −77.2201 | −3.19539 | ||||||||
\(585\) | −41.1997 | −1.70340 | ||||||||
\(586\) | −14.9550 | −0.617785 | ||||||||
\(587\) | −4.81384 | −0.198688 | −0.0993442 | − | 0.995053i | \(-0.531674\pi\) | ||||
−0.0993442 | + | 0.995053i | \(0.531674\pi\) | |||||||
\(588\) | −263.432 | −10.8637 | ||||||||
\(589\) | −10.5223 | −0.433564 | ||||||||
\(590\) | 43.2913 | 1.78228 | ||||||||
\(591\) | −13.1363 | −0.540353 | ||||||||
\(592\) | −19.0189 | −0.781673 | ||||||||
\(593\) | 33.3451 | 1.36932 | 0.684660 | − | 0.728862i | \(-0.259951\pi\) | ||||
0.684660 | + | 0.728862i | \(0.259951\pi\) | |||||||
\(594\) | −11.9814 | −0.491603 | ||||||||
\(595\) | −58.7777 | −2.40965 | ||||||||
\(596\) | 98.6266 | 4.03990 | ||||||||
\(597\) | 5.94123 | 0.243158 | ||||||||
\(598\) | −12.4783 | −0.510277 | ||||||||
\(599\) | 9.78236 | 0.399696 | 0.199848 | − | 0.979827i | \(-0.435955\pi\) | ||||
0.199848 | + | 0.979827i | \(0.435955\pi\) | |||||||
\(600\) | 116.937 | 4.77391 | ||||||||
\(601\) | 46.9041 | 1.91326 | 0.956629 | − | 0.291310i | \(-0.0940911\pi\) | ||||
0.956629 | + | 0.291310i | \(0.0940911\pi\) | |||||||
\(602\) | 63.9219 | 2.60526 | ||||||||
\(603\) | −60.7366 | −2.47339 | ||||||||
\(604\) | −47.7045 | −1.94107 | ||||||||
\(605\) | −27.6471 | −1.12401 | ||||||||
\(606\) | −24.4076 | −0.991493 | ||||||||
\(607\) | −31.5165 | −1.27921 | −0.639607 | − | 0.768702i | \(-0.720903\pi\) | ||||
−0.639607 | + | 0.768702i | \(0.720903\pi\) | |||||||
\(608\) | −140.581 | −5.70130 | ||||||||
\(609\) | −77.3527 | −3.13449 | ||||||||
\(610\) | 114.002 | 4.61580 | ||||||||
\(611\) | 24.8202 | 1.00412 | ||||||||
\(612\) | −99.8466 | −4.03606 | ||||||||
\(613\) | 3.67915 | 0.148600 | 0.0742998 | − | 0.997236i | \(-0.476328\pi\) | ||||
0.0742998 | + | 0.997236i | \(0.476328\pi\) | |||||||
\(614\) | −29.8334 | −1.20398 | ||||||||
\(615\) | 59.6569 | 2.40560 | ||||||||
\(616\) | 70.9760 | 2.85970 | ||||||||
\(617\) | −6.17204 | −0.248477 | −0.124239 | − | 0.992252i | \(-0.539649\pi\) | ||||
−0.124239 | + | 0.992252i | \(0.539649\pi\) | |||||||
\(618\) | 52.2167 | 2.10046 | ||||||||
\(619\) | −12.9977 | −0.522420 | −0.261210 | − | 0.965282i | \(-0.584121\pi\) | ||||
−0.261210 | + | 0.965282i | \(0.584121\pi\) | |||||||
\(620\) | −41.7223 | −1.67561 | ||||||||
\(621\) | 4.33518 | 0.173965 | ||||||||
\(622\) | −60.1166 | −2.41046 | ||||||||
\(623\) | 6.08231 | 0.243683 | ||||||||
\(624\) | 167.264 | 6.69592 | ||||||||
\(625\) | −29.0709 | −1.16284 | ||||||||
\(626\) | 52.1755 | 2.08535 | ||||||||
\(627\) | 15.9195 | 0.635764 | ||||||||
\(628\) | 30.4740 | 1.21605 | ||||||||
\(629\) | 4.03462 | 0.160871 | ||||||||
\(630\) | −171.736 | −6.84211 | ||||||||
\(631\) | −38.7519 | −1.54269 | −0.771344 | − | 0.636418i | \(-0.780415\pi\) | ||||
−0.771344 | + | 0.636418i | \(0.780415\pi\) | |||||||
\(632\) | −154.721 | −6.15448 | ||||||||
\(633\) | −47.5652 | −1.89055 | ||||||||
\(634\) | −3.38097 | −0.134275 | ||||||||
\(635\) | −46.3775 | −1.84044 | ||||||||
\(636\) | −42.0555 | −1.66761 | ||||||||
\(637\) | −54.5764 | −2.16240 | ||||||||
\(638\) | 22.1928 | 0.878622 | ||||||||
\(639\) | −46.2755 | −1.83063 | ||||||||
\(640\) | −237.090 | −9.37180 | ||||||||
\(641\) | −7.05938 | −0.278829 | −0.139414 | − | 0.990234i | \(-0.544522\pi\) | ||||
−0.139414 | + | 0.990234i | \(0.544522\pi\) | |||||||
\(642\) | 17.1325 | 0.676167 | ||||||||
\(643\) | −15.2687 | −0.602140 | −0.301070 | − | 0.953602i | \(-0.597344\pi\) | ||||
−0.301070 | + | 0.953602i | \(0.597344\pi\) | |||||||
\(644\) | −38.8476 | −1.53081 | ||||||||
\(645\) | 37.5814 | 1.47977 | ||||||||
\(646\) | 50.5648 | 1.98944 | ||||||||
\(647\) | −28.4191 | −1.11727 | −0.558635 | − | 0.829414i | \(-0.688675\pi\) | ||||
−0.558635 | + | 0.829414i | \(0.688675\pi\) | |||||||
\(648\) | 43.7854 | 1.72005 | ||||||||
\(649\) | 6.84320 | 0.268619 | ||||||||
\(650\) | 36.6472 | 1.43742 | ||||||||
\(651\) | 30.7786 | 1.20631 | ||||||||
\(652\) | 54.2696 | 2.12536 | ||||||||
\(653\) | 41.4163 | 1.62074 | 0.810372 | − | 0.585916i | \(-0.199265\pi\) | ||||
0.810372 | + | 0.585916i | \(0.199265\pi\) | |||||||
\(654\) | −7.53909 | −0.294802 | ||||||||
\(655\) | −62.2606 | −2.43272 | ||||||||
\(656\) | −141.195 | −5.51276 | ||||||||
\(657\) | 29.5350 | 1.15227 | ||||||||
\(658\) | 103.460 | 4.03328 | ||||||||
\(659\) | 14.2736 | 0.556020 | 0.278010 | − | 0.960578i | \(-0.410325\pi\) | ||||
0.278010 | + | 0.960578i | \(0.410325\pi\) | |||||||
\(660\) | 63.1230 | 2.45706 | ||||||||
\(661\) | −15.6146 | −0.607337 | −0.303668 | − | 0.952778i | \(-0.598212\pi\) | ||||
−0.303668 | + | 0.952778i | \(0.598212\pi\) | |||||||
\(662\) | 31.0674 | 1.20747 | ||||||||
\(663\) | −35.4829 | −1.37804 | ||||||||
\(664\) | −27.7456 | −1.07674 | ||||||||
\(665\) | 64.9556 | 2.51887 | ||||||||
\(666\) | 11.7883 | 0.456786 | ||||||||
\(667\) | −8.02994 | −0.310920 | ||||||||
\(668\) | 4.75520 | 0.183984 | ||||||||
\(669\) | 46.7429 | 1.80719 | ||||||||
\(670\) | 121.962 | 4.71179 | ||||||||
\(671\) | 18.0207 | 0.695680 | ||||||||
\(672\) | 411.210 | 15.8628 | ||||||||
\(673\) | −20.4865 | −0.789696 | −0.394848 | − | 0.918747i | \(-0.629203\pi\) | ||||
−0.394848 | + | 0.918747i | \(0.629203\pi\) | |||||||
\(674\) | −17.6405 | −0.679488 | ||||||||
\(675\) | −12.7318 | −0.490049 | ||||||||
\(676\) | −13.2676 | −0.510292 | ||||||||
\(677\) | 45.4249 | 1.74582 | 0.872911 | − | 0.487880i | \(-0.162230\pi\) | ||||
0.872911 | + | 0.487880i | \(0.162230\pi\) | |||||||
\(678\) | −105.917 | −4.06773 | ||||||||
\(679\) | −55.2567 | −2.12056 | ||||||||
\(680\) | 132.542 | 5.08275 | ||||||||
\(681\) | 11.4310 | 0.438037 | ||||||||
\(682\) | −8.83050 | −0.338137 | ||||||||
\(683\) | 27.3934 | 1.04818 | 0.524090 | − | 0.851663i | \(-0.324406\pi\) | ||||
0.524090 | + | 0.851663i | \(0.324406\pi\) | |||||||
\(684\) | 110.341 | 4.21900 | ||||||||
\(685\) | 40.5797 | 1.55047 | ||||||||
\(686\) | −131.819 | −5.03288 | ||||||||
\(687\) | −49.6834 | −1.89554 | ||||||||
\(688\) | −88.9473 | −3.39109 | ||||||||
\(689\) | −8.71284 | −0.331933 | ||||||||
\(690\) | −30.5806 | −1.16418 | ||||||||
\(691\) | −7.67251 | −0.291876 | −0.145938 | − | 0.989294i | \(-0.546620\pi\) | ||||
−0.145938 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(692\) | −121.823 | −4.63102 | ||||||||
\(693\) | −27.1468 | −1.03122 | ||||||||
\(694\) | −27.7421 | −1.05307 | ||||||||
\(695\) | −29.4438 | −1.11687 | ||||||||
\(696\) | 174.428 | 6.61167 | ||||||||
\(697\) | 29.9528 | 1.13454 | ||||||||
\(698\) | 22.2654 | 0.842759 | ||||||||
\(699\) | −35.5756 | −1.34559 | ||||||||
\(700\) | 114.090 | 4.31221 | ||||||||
\(701\) | 5.82316 | 0.219938 | 0.109969 | − | 0.993935i | \(-0.464925\pi\) | ||||
0.109969 | + | 0.993935i | \(0.464925\pi\) | |||||||
\(702\) | −29.5122 | −1.11387 | ||||||||
\(703\) | −4.45868 | −0.168162 | ||||||||
\(704\) | −67.3419 | −2.53804 | ||||||||
\(705\) | 60.8268 | 2.29087 | ||||||||
\(706\) | −46.6345 | −1.75511 | ||||||||
\(707\) | −15.7424 | −0.592054 | ||||||||
\(708\) | 81.3610 | 3.05773 | ||||||||
\(709\) | −49.6360 | −1.86412 | −0.932059 | − | 0.362306i | \(-0.881990\pi\) | ||||
−0.932059 | + | 0.362306i | \(0.881990\pi\) | |||||||
\(710\) | 92.9231 | 3.48734 | ||||||||
\(711\) | 59.1776 | 2.21933 | ||||||||
\(712\) | −13.7154 | −0.514007 | ||||||||
\(713\) | 3.19511 | 0.119658 | ||||||||
\(714\) | −147.906 | −5.53524 | ||||||||
\(715\) | 13.0775 | 0.489071 | ||||||||
\(716\) | 36.6514 | 1.36973 | ||||||||
\(717\) | −3.13270 | −0.116993 | ||||||||
\(718\) | −71.5837 | −2.67148 | ||||||||
\(719\) | 31.9469 | 1.19142 | 0.595710 | − | 0.803200i | \(-0.296871\pi\) | ||||
0.595710 | + | 0.803200i | \(0.296871\pi\) | |||||||
\(720\) | 238.970 | 8.90588 | ||||||||
\(721\) | 33.6786 | 1.25426 | ||||||||
\(722\) | −2.47317 | −0.0920419 | ||||||||
\(723\) | −47.6995 | −1.77396 | ||||||||
\(724\) | −18.7174 | −0.695627 | ||||||||
\(725\) | 23.5829 | 0.875845 | ||||||||
\(726\) | −69.5700 | −2.58199 | ||||||||
\(727\) | −26.9356 | −0.998985 | −0.499492 | − | 0.866318i | \(-0.666480\pi\) | ||||
−0.499492 | + | 0.866318i | \(0.666480\pi\) | |||||||
\(728\) | 174.826 | 6.47947 | ||||||||
\(729\) | −42.5118 | −1.57451 | ||||||||
\(730\) | −59.3075 | −2.19507 | ||||||||
\(731\) | 18.8690 | 0.697897 | ||||||||
\(732\) | 214.253 | 7.91902 | ||||||||
\(733\) | −46.9660 | −1.73473 | −0.867364 | − | 0.497674i | \(-0.834188\pi\) | ||||
−0.867364 | + | 0.497674i | \(0.834188\pi\) | |||||||
\(734\) | −75.2876 | −2.77892 | ||||||||
\(735\) | −133.750 | −4.93345 | ||||||||
\(736\) | 42.6875 | 1.57348 | ||||||||
\(737\) | 19.2789 | 0.710146 | ||||||||
\(738\) | 87.5155 | 3.22149 | ||||||||
\(739\) | 38.7073 | 1.42387 | 0.711935 | − | 0.702245i | \(-0.247819\pi\) | ||||
0.711935 | + | 0.702245i | \(0.247819\pi\) | |||||||
\(740\) | −17.6793 | −0.649903 | ||||||||
\(741\) | 39.2124 | 1.44050 | ||||||||
\(742\) | −36.3184 | −1.33329 | ||||||||
\(743\) | −33.0476 | −1.21240 | −0.606200 | − | 0.795312i | \(-0.707307\pi\) | ||||
−0.606200 | + | 0.795312i | \(0.707307\pi\) | |||||||
\(744\) | −69.4047 | −2.54450 | ||||||||
\(745\) | 50.0750 | 1.83461 | ||||||||
\(746\) | 17.7510 | 0.649910 | ||||||||
\(747\) | 10.6121 | 0.388276 | ||||||||
\(748\) | 31.6931 | 1.15881 | ||||||||
\(749\) | 11.0501 | 0.403762 | ||||||||
\(750\) | −23.1255 | −0.844424 | ||||||||
\(751\) | −20.4705 | −0.746978 | −0.373489 | − | 0.927635i | \(-0.621839\pi\) | ||||
−0.373489 | + | 0.927635i | \(0.621839\pi\) | |||||||
\(752\) | −143.964 | −5.24983 | ||||||||
\(753\) | 40.2694 | 1.46750 | ||||||||
\(754\) | 54.6646 | 1.99077 | ||||||||
\(755\) | −24.2207 | −0.881480 | ||||||||
\(756\) | −91.8775 | −3.34155 | ||||||||
\(757\) | 49.7058 | 1.80659 | 0.903295 | − | 0.429021i | \(-0.141141\pi\) | ||||
0.903295 | + | 0.429021i | \(0.141141\pi\) | |||||||
\(758\) | −1.78059 | −0.0646739 | ||||||||
\(759\) | −4.83397 | −0.175462 | ||||||||
\(760\) | −146.473 | −5.31312 | ||||||||
\(761\) | −44.6502 | −1.61857 | −0.809284 | − | 0.587418i | \(-0.800145\pi\) | ||||
−0.809284 | + | 0.587418i | \(0.800145\pi\) | |||||||
\(762\) | −116.703 | −4.22769 | ||||||||
\(763\) | −4.86255 | −0.176036 | ||||||||
\(764\) | −149.296 | −5.40133 | ||||||||
\(765\) | −50.6944 | −1.83286 | ||||||||
\(766\) | 86.2243 | 3.11541 | ||||||||
\(767\) | 16.8560 | 0.608633 | ||||||||
\(768\) | −325.239 | −11.7361 | ||||||||
\(769\) | 1.02444 | 0.0369424 | 0.0184712 | − | 0.999829i | \(-0.494120\pi\) | ||||
0.0184712 | + | 0.999829i | \(0.494120\pi\) | |||||||
\(770\) | 54.5119 | 1.96447 | ||||||||
\(771\) | 5.76205 | 0.207515 | ||||||||
\(772\) | −50.7594 | −1.82687 | ||||||||
\(773\) | 6.51487 | 0.234324 | 0.117162 | − | 0.993113i | \(-0.462620\pi\) | ||||
0.117162 | + | 0.993113i | \(0.462620\pi\) | |||||||
\(774\) | 55.1312 | 1.98165 | ||||||||
\(775\) | −9.38360 | −0.337069 | ||||||||
\(776\) | 124.602 | 4.47296 | ||||||||
\(777\) | 13.0420 | 0.467880 | ||||||||
\(778\) | 57.4579 | 2.05997 | ||||||||
\(779\) | −33.1010 | −1.18597 | ||||||||
\(780\) | 155.483 | 5.56717 | ||||||||
\(781\) | 14.6887 | 0.525602 | ||||||||
\(782\) | −15.3540 | −0.549059 | ||||||||
\(783\) | −18.9914 | −0.678697 | ||||||||
\(784\) | 316.559 | 11.3057 | ||||||||
\(785\) | 15.4723 | 0.552232 | ||||||||
\(786\) | −156.670 | −5.58824 | ||||||||
\(787\) | 6.86513 | 0.244716 | 0.122358 | − | 0.992486i | \(-0.460954\pi\) | ||||
0.122358 | + | 0.992486i | \(0.460954\pi\) | |||||||
\(788\) | 28.9008 | 1.02955 | ||||||||
\(789\) | 0.161766 | 0.00575903 | ||||||||
\(790\) | −118.831 | −4.22782 | ||||||||
\(791\) | −68.3145 | −2.42898 | ||||||||
\(792\) | 61.2152 | 2.17519 | ||||||||
\(793\) | 44.3879 | 1.57626 | ||||||||
\(794\) | −37.6074 | −1.33464 | ||||||||
\(795\) | −21.3525 | −0.757296 | ||||||||
\(796\) | −13.0712 | −0.463296 | ||||||||
\(797\) | −43.9442 | −1.55658 | −0.778291 | − | 0.627903i | \(-0.783913\pi\) | ||||
−0.778291 | + | 0.627903i | \(0.783913\pi\) | |||||||
\(798\) | 163.452 | 5.78613 | ||||||||
\(799\) | 30.5402 | 1.08043 | ||||||||
\(800\) | −125.367 | −4.43240 | ||||||||
\(801\) | 5.24585 | 0.185353 | ||||||||
\(802\) | −58.6415 | −2.07070 | ||||||||
\(803\) | −9.37494 | −0.330834 | ||||||||
\(804\) | 229.212 | 8.08370 | ||||||||
\(805\) | −19.7238 | −0.695173 | ||||||||
\(806\) | −21.7510 | −0.766146 | ||||||||
\(807\) | −69.6304 | −2.45111 | ||||||||
\(808\) | 35.4986 | 1.24884 | ||||||||
\(809\) | 31.0335 | 1.09108 | 0.545540 | − | 0.838085i | \(-0.316325\pi\) | ||||
0.545540 | + | 0.838085i | \(0.316325\pi\) | |||||||
\(810\) | 33.6286 | 1.18159 | ||||||||
\(811\) | −31.9230 | −1.12097 | −0.560484 | − | 0.828165i | \(-0.689385\pi\) | ||||
−0.560484 | + | 0.828165i | \(0.689385\pi\) | |||||||
\(812\) | 170.182 | 5.97223 | ||||||||
\(813\) | 5.79907 | 0.203382 | ||||||||
\(814\) | −3.74181 | −0.131150 | ||||||||
\(815\) | 27.5539 | 0.965172 | ||||||||
\(816\) | 205.811 | 7.20483 | ||||||||
\(817\) | −20.8523 | −0.729529 | ||||||||
\(818\) | −53.1779 | −1.85932 | ||||||||
\(819\) | −66.8671 | −2.33653 | ||||||||
\(820\) | −131.250 | −4.58345 | ||||||||
\(821\) | −12.2379 | −0.427106 | −0.213553 | − | 0.976931i | \(-0.568504\pi\) | ||||
−0.213553 | + | 0.976931i | \(0.568504\pi\) | |||||||
\(822\) | 102.113 | 3.56161 | ||||||||
\(823\) | −33.0179 | −1.15093 | −0.575466 | − | 0.817826i | \(-0.695179\pi\) | ||||
−0.575466 | + | 0.817826i | \(0.695179\pi\) | |||||||
\(824\) | −75.9442 | −2.64564 | ||||||||
\(825\) | 14.1967 | 0.494267 | ||||||||
\(826\) | 70.2618 | 2.44472 | ||||||||
\(827\) | 27.2516 | 0.947632 | 0.473816 | − | 0.880624i | \(-0.342876\pi\) | ||||
0.473816 | + | 0.880624i | \(0.342876\pi\) | |||||||
\(828\) | −33.5052 | −1.16439 | ||||||||
\(829\) | 12.8356 | 0.445797 | 0.222899 | − | 0.974842i | \(-0.428448\pi\) | ||||
0.222899 | + | 0.974842i | \(0.428448\pi\) | |||||||
\(830\) | −21.3095 | −0.739664 | ||||||||
\(831\) | −6.68891 | −0.232036 | ||||||||
\(832\) | −165.874 | −5.75066 | ||||||||
\(833\) | −67.1539 | −2.32674 | ||||||||
\(834\) | −74.0914 | −2.56557 | ||||||||
\(835\) | 2.41432 | 0.0835510 | ||||||||
\(836\) | −35.0242 | −1.21134 | ||||||||
\(837\) | 7.55666 | 0.261197 | ||||||||
\(838\) | −17.6784 | −0.610689 | ||||||||
\(839\) | −23.4493 | −0.809559 | −0.404779 | − | 0.914414i | \(-0.632652\pi\) | ||||
−0.404779 | + | 0.914414i | \(0.632652\pi\) | |||||||
\(840\) | 428.445 | 14.7827 | ||||||||
\(841\) | 6.17726 | 0.213009 | ||||||||
\(842\) | 10.8968 | 0.375529 | ||||||||
\(843\) | −65.9848 | −2.27264 | ||||||||
\(844\) | 104.647 | 3.60211 | ||||||||
\(845\) | −6.73626 | −0.231734 | ||||||||
\(846\) | 89.2317 | 3.06785 | ||||||||
\(847\) | −44.8712 | −1.54179 | ||||||||
\(848\) | 50.5370 | 1.73545 | ||||||||
\(849\) | 81.8816 | 2.81017 | ||||||||
\(850\) | 45.0927 | 1.54667 | ||||||||
\(851\) | 1.35388 | 0.0464105 | ||||||||
\(852\) | 174.638 | 5.98300 | ||||||||
\(853\) | 38.2265 | 1.30885 | 0.654425 | − | 0.756127i | \(-0.272911\pi\) | ||||
0.654425 | + | 0.756127i | \(0.272911\pi\) | |||||||
\(854\) | 185.025 | 6.33143 | ||||||||
\(855\) | 56.0227 | 1.91594 | ||||||||
\(856\) | −24.9176 | −0.851667 | ||||||||
\(857\) | −5.05588 | −0.172705 | −0.0863527 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863527 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(858\) | 32.9078 | 1.12345 | ||||||||
\(859\) | 29.9075 | 1.02043 | 0.510216 | − | 0.860046i | \(-0.329565\pi\) | ||||
0.510216 | + | 0.860046i | \(0.329565\pi\) | |||||||
\(860\) | −82.6821 | −2.81944 | ||||||||
\(861\) | 96.8232 | 3.29973 | ||||||||
\(862\) | 98.2065 | 3.34493 | ||||||||
\(863\) | −48.1847 | −1.64023 | −0.820113 | − | 0.572202i | \(-0.806089\pi\) | ||||
−0.820113 | + | 0.572202i | \(0.806089\pi\) | |||||||
\(864\) | 100.959 | 3.43470 | ||||||||
\(865\) | −61.8523 | −2.10304 | ||||||||
\(866\) | 14.6205 | 0.496825 | ||||||||
\(867\) | 1.93607 | 0.0657523 | ||||||||
\(868\) | −67.7154 | −2.29841 | ||||||||
\(869\) | −18.7840 | −0.637204 | ||||||||
\(870\) | 133.966 | 4.54188 | ||||||||
\(871\) | 47.4871 | 1.60904 | ||||||||
\(872\) | 10.9649 | 0.371318 | ||||||||
\(873\) | −47.6577 | −1.61297 | ||||||||
\(874\) | 16.9678 | 0.573946 | ||||||||
\(875\) | −14.9155 | −0.504234 | ||||||||
\(876\) | −111.462 | −3.76594 | ||||||||
\(877\) | 7.89519 | 0.266602 | 0.133301 | − | 0.991076i | \(-0.457442\pi\) | ||||
0.133301 | + | 0.991076i | \(0.457442\pi\) | |||||||
\(878\) | −60.0036 | −2.02502 | ||||||||
\(879\) | −14.2701 | −0.481320 | ||||||||
\(880\) | −75.8533 | −2.55701 | ||||||||
\(881\) | −5.03885 | −0.169763 | −0.0848816 | − | 0.996391i | \(-0.527051\pi\) | ||||
−0.0848816 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(882\) | −196.209 | −6.60670 | ||||||||
\(883\) | 2.45026 | 0.0824578 | 0.0412289 | − | 0.999150i | \(-0.486873\pi\) | ||||
0.0412289 | + | 0.999150i | \(0.486873\pi\) | |||||||
\(884\) | 78.0653 | 2.62562 | ||||||||
\(885\) | 41.3088 | 1.38858 | ||||||||
\(886\) | −109.376 | −3.67457 | ||||||||
\(887\) | 43.1676 | 1.44943 | 0.724713 | − | 0.689050i | \(-0.241972\pi\) | ||||
0.724713 | + | 0.689050i | \(0.241972\pi\) | |||||||
\(888\) | −29.4093 | −0.986912 | ||||||||
\(889\) | −75.2707 | −2.52450 | ||||||||
\(890\) | −10.5339 | −0.353096 | ||||||||
\(891\) | 5.31578 | 0.178085 | ||||||||
\(892\) | −102.838 | −3.44328 | ||||||||
\(893\) | −33.7501 | −1.12940 | ||||||||
\(894\) | 126.007 | 4.21430 | ||||||||
\(895\) | 18.6088 | 0.622022 | ||||||||
\(896\) | −384.797 | −12.8552 | ||||||||
\(897\) | −11.9069 | −0.397559 | ||||||||
\(898\) | 6.74432 | 0.225061 | ||||||||
\(899\) | −13.9970 | −0.466826 | ||||||||
\(900\) | 98.4002 | 3.28001 | ||||||||
\(901\) | −10.7208 | −0.357161 | ||||||||
\(902\) | −27.7790 | −0.924939 | ||||||||
\(903\) | 60.9946 | 2.02977 | ||||||||
\(904\) | 154.047 | 5.12352 | ||||||||
\(905\) | −9.50325 | −0.315899 | ||||||||
\(906\) | −60.9480 | −2.02486 | ||||||||
\(907\) | −21.3727 | −0.709670 | −0.354835 | − | 0.934929i | \(-0.615463\pi\) | ||||
−0.354835 | + | 0.934929i | \(0.615463\pi\) | |||||||
\(908\) | −25.1491 | −0.834603 | ||||||||
\(909\) | −13.5775 | −0.450336 | ||||||||
\(910\) | 134.272 | 4.45107 | ||||||||
\(911\) | 3.86748 | 0.128135 | 0.0640677 | − | 0.997946i | \(-0.479593\pi\) | ||||
0.0640677 | + | 0.997946i | \(0.479593\pi\) | |||||||
\(912\) | −227.443 | −7.53140 | ||||||||
\(913\) | −3.36846 | −0.111480 | ||||||||
\(914\) | −74.0316 | −2.44875 | ||||||||
\(915\) | 108.781 | 3.59619 | ||||||||
\(916\) | 109.308 | 3.61162 | ||||||||
\(917\) | −101.049 | −3.33693 | ||||||||
\(918\) | −36.3134 | −1.19852 | ||||||||
\(919\) | 35.3232 | 1.16521 | 0.582603 | − | 0.812757i | \(-0.302034\pi\) | ||||
0.582603 | + | 0.812757i | \(0.302034\pi\) | |||||||
\(920\) | 44.4766 | 1.46635 | ||||||||
\(921\) | −28.4672 | −0.938026 | ||||||||
\(922\) | 18.6221 | 0.613286 | ||||||||
\(923\) | 36.1806 | 1.19090 | ||||||||
\(924\) | 102.449 | 3.37031 | ||||||||
\(925\) | −3.97617 | −0.130736 | ||||||||
\(926\) | 16.6888 | 0.548429 | ||||||||
\(927\) | 29.0470 | 0.954030 | ||||||||
\(928\) | −187.004 | −6.13870 | ||||||||
\(929\) | −44.3052 | −1.45361 | −0.726803 | − | 0.686846i | \(-0.758995\pi\) | ||||
−0.726803 | + | 0.686846i | \(0.758995\pi\) | |||||||
\(930\) | −53.3051 | −1.74794 | ||||||||
\(931\) | 74.2122 | 2.43221 | ||||||||
\(932\) | 78.2693 | 2.56379 | ||||||||
\(933\) | −57.3636 | −1.87800 | ||||||||
\(934\) | 63.4428 | 2.07591 | ||||||||
\(935\) | 16.0913 | 0.526242 | ||||||||
\(936\) | 150.783 | 4.92850 | ||||||||
\(937\) | 5.55481 | 0.181468 | 0.0907339 | − | 0.995875i | \(-0.471079\pi\) | ||||
0.0907339 | + | 0.995875i | \(0.471079\pi\) | |||||||
\(938\) | 197.944 | 6.46309 | ||||||||
\(939\) | 49.7861 | 1.62471 | ||||||||
\(940\) | −133.824 | −4.36485 | ||||||||
\(941\) | 39.7310 | 1.29520 | 0.647598 | − | 0.761983i | \(-0.275774\pi\) | ||||
0.647598 | + | 0.761983i | \(0.275774\pi\) | |||||||
\(942\) | 38.9340 | 1.26854 | ||||||||
\(943\) | 10.0512 | 0.327311 | ||||||||
\(944\) | −97.7693 | −3.18212 | ||||||||
\(945\) | −46.6483 | −1.51747 | ||||||||
\(946\) | −17.4996 | −0.568961 | ||||||||
\(947\) | 2.06859 | 0.0672203 | 0.0336101 | − | 0.999435i | \(-0.489300\pi\) | ||||
0.0336101 | + | 0.999435i | \(0.489300\pi\) | |||||||
\(948\) | −223.329 | −7.25338 | ||||||||
\(949\) | −23.0920 | −0.749599 | ||||||||
\(950\) | −49.8323 | −1.61677 | ||||||||
\(951\) | −3.22613 | −0.104615 | ||||||||
\(952\) | 215.115 | 6.97193 | ||||||||
\(953\) | −23.7937 | −0.770754 | −0.385377 | − | 0.922759i | \(-0.625929\pi\) | ||||
−0.385377 | + | 0.922759i | \(0.625929\pi\) | |||||||
\(954\) | −31.3237 | −1.01414 | ||||||||
\(955\) | −75.8008 | −2.45286 | ||||||||
\(956\) | 6.89220 | 0.222910 | ||||||||
\(957\) | 21.1765 | 0.684539 | ||||||||
\(958\) | 115.684 | 3.73757 | ||||||||
\(959\) | 65.8609 | 2.12676 | ||||||||
\(960\) | −406.508 | −13.1200 | ||||||||
\(961\) | −25.4306 | −0.820342 | ||||||||
\(962\) | −9.21669 | −0.297158 | ||||||||
\(963\) | 9.53047 | 0.307115 | ||||||||
\(964\) | 104.943 | 3.37998 | ||||||||
\(965\) | −25.7717 | −0.829620 | ||||||||
\(966\) | −49.6323 | −1.59689 | ||||||||
\(967\) | 22.6454 | 0.728227 | 0.364114 | − | 0.931354i | \(-0.381372\pi\) | ||||
0.364114 | + | 0.931354i | \(0.381372\pi\) | |||||||
\(968\) | 101.183 | 3.25215 | ||||||||
\(969\) | 48.2492 | 1.54999 | ||||||||
\(970\) | 95.6985 | 3.07269 | ||||||||
\(971\) | −47.5343 | −1.52545 | −0.762724 | − | 0.646724i | \(-0.776139\pi\) | ||||
−0.762724 | + | 0.646724i | \(0.776139\pi\) | |||||||
\(972\) | 119.886 | 3.84534 | ||||||||
\(973\) | −47.7873 | −1.53199 | ||||||||
\(974\) | 18.7380 | 0.600404 | ||||||||
\(975\) | 34.9689 | 1.11990 | ||||||||
\(976\) | −257.462 | −8.24117 | ||||||||
\(977\) | 10.9522 | 0.350392 | 0.175196 | − | 0.984534i | \(-0.443944\pi\) | ||||
0.175196 | + | 0.984534i | \(0.443944\pi\) | |||||||
\(978\) | 69.3357 | 2.21711 | ||||||||
\(979\) | −1.66513 | −0.0532176 | ||||||||
\(980\) | 294.261 | 9.39983 | ||||||||
\(981\) | −4.19384 | −0.133899 | ||||||||
\(982\) | 20.5658 | 0.656281 | ||||||||
\(983\) | −0.953264 | −0.0304044 | −0.0152022 | − | 0.999884i | \(-0.504839\pi\) | ||||
−0.0152022 | + | 0.999884i | \(0.504839\pi\) | |||||||
\(984\) | −218.333 | −6.96021 | ||||||||
\(985\) | 14.6736 | 0.467540 | ||||||||
\(986\) | 67.2624 | 2.14207 | ||||||||
\(987\) | 98.7218 | 3.14235 | ||||||||
\(988\) | −86.2705 | −2.74463 | ||||||||
\(989\) | 6.33182 | 0.201340 | ||||||||
\(990\) | 47.0152 | 1.49424 | ||||||||
\(991\) | −15.6137 | −0.495986 | −0.247993 | − | 0.968762i | \(-0.579771\pi\) | ||||
−0.247993 | + | 0.968762i | \(0.579771\pi\) | |||||||
\(992\) | 74.4086 | 2.36248 | ||||||||
\(993\) | 29.6447 | 0.940745 | ||||||||
\(994\) | 150.814 | 4.78354 | ||||||||
\(995\) | −6.63654 | −0.210392 | ||||||||
\(996\) | −40.0487 | −1.26899 | ||||||||
\(997\) | 24.6809 | 0.781653 | 0.390826 | − | 0.920464i | \(-0.372189\pi\) | ||||
0.390826 | + | 0.920464i | \(0.372189\pi\) | |||||||
\(998\) | 51.1240 | 1.61830 | ||||||||
\(999\) | 3.20203 | 0.101308 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4033.2.a.d.1.1 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.1 | ✓ | 79 | 1.1 | even | 1 | trivial |